JAMB 1988 · UME · Q37

In the figure, $PS = RS = QS$ and $\angle QSR = 50^\circ$ . Find $\angle QPR$ .

Worked solution (try it first)

$SP = SQ = SR$ , so $P$ , $Q$ and $R$ lie on a circle with centre $S$ .
$\angle QSR$ is the angle at the centre on arc $QR$ , and $\angle QPR$ is the angle at the circumference on the same arc.
The angle at the circumference is half the angle at the centre: $\angle QPR = \frac12 \times 50^\circ$
$= 25^\circ$ , option A.